Fix overflow bug in standard deviation computation. (#10100)

Summary:
There was an overflow bug when computing the variance in the HistogramStat class.

This manifests, for instance, when running cache_bench with default arguments. This executes 32M lookups/inserts/deletes in a block cache, and then computes (among other things) the variance of the latencies. The variance is computed as ``variance = (cur_sum_squares * cur_num - cur_sum * cur_sum) / (cur_num * cur_num)``, where ``cum_sum_squares`` is the sum of the squares of the samples, ``cur_num`` is the number of samples, and ``cur_sum`` is the sum of the samples. Because the median latency in a typical run is around 3800 nanoseconds, both the ``cur_sum_squares * cur_num`` and ``cur_sum * cur_sum`` terms overflow as uint64_t.

Pull Request resolved: https://github.com/facebook/rocksdb/pull/10100

Test Plan: Added a unit test. Run ``make -j24 histogram_test && ./histogram_test``.

Reviewed By: pdillinger

Differential Revision: D36942738

Pulled By: guidotag

fbshipit-source-id: 0af5fb9e2a297a284e8e74c24e604d302906006e

monitoring/histogram.cc

@@ -164,15 +164,16 @@ double HistogramStat::Average() const {
 }
 
 double HistogramStat::StandardDeviation() const {
-  uint64_t cur_num = num();
-  uint64_t cur_sum = sum();
-  uint64_t cur_sum_squares = sum_squares();
+  double cur_num =
+      static_cast<double>(num());  // Use double to avoid integer overflow
+  double cur_sum = static_cast<double>(sum());
+  double cur_sum_squares = static_cast<double>(sum_squares());
   if (cur_num == 0) return 0;
   double variance =
-      static_cast<double>(cur_sum_squares * cur_num - cur_sum * cur_sum) /
-      static_cast<double>(cur_num * cur_num);
+      (cur_sum_squares * cur_num - cur_sum * cur_sum) / (cur_num * cur_num);
   return std::sqrt(variance);
 }
+
 std::string HistogramStat::ToString() const {
   uint64_t cur_num = num();
   std::string r;

monitoring/histogram_test.cc

@@ -225,6 +225,12 @@ TEST_F(HistogramTest, HistogramWindowingMerge) {
   ASSERT_EQ(histogramWindowing.max(), 5);
 }
 
+TEST_F(HistogramTest, LargeStandardDeviation) {
+  HistogramImpl histogram;
+  PopulateHistogram(histogram, 1, 1000000);
+  ASSERT_LT(fabs(histogram.StandardDeviation() - 288675), 1);
+}
+
 }  // namespace ROCKSDB_NAMESPACE
 
 int main(int argc, char** argv) {